It is readily to shown that by restricting the estimation at the PS to be linear, the OTA-FL scheme is optimal: there exists a receiver \(\mathbf {m}\)  and scaling coefficients \(b_\ell \)  whose corresponding estimate of global model, i.e., \(\hat{\theta }\)  in (REF ), recovers the estimate achieved by combining the optimal linear estimation of local models according to the predefined strategy in (REF ) [1]}.
